Bisimulation metrics are powerful tools for measuring similarities between stochastic processes, and specifically Markov chains. Recent advances have uncovered that bisimulation metrics are, in fact, optimal-transport distances, which has enabled the development of fast algorithms for computing such metrics with provable accuracy and runtime guarantees. However, these recent methods, as well as all previously known methods, assume full knowledge of the transition dynamics. This is often an impractical assumption in most real-world scenarios, where typically only sample trajectories are available. In this work, we propose a stochastic optimization method that addresses this limitation and estimates bisimulation metrics based on sample access, without requiring explicit transition models. Our approach is derived from a new linear programming (LP) formulation of bisimulation metrics, which we solve using a stochastic primal-dual optimization method. We provide theoretical guarantees on the sample complexity of the algorithm and validate its effectiveness through a series of empirical evaluations.

We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction to dynamic programming (DP) in an appropriately defined Markov decision process. This formulation has, however, not led to particularly efficient algorithms so far, since computing the associated DP operators requires fully solving a static optimal transport problem, and these operators need to be applied numerous times during the overall optimization process. In this work, we develop an alternative perspective by considering couplings between a ``flattened'' version of the joint distributions that we call discounted occupancy couplings, and show that calculating optimal transport distances in the full space of joint distributions can be equivalently formulated as solving a linear program (LP) in this reduced space. This LP formulation formulation allows us to port several algorithmic ideas from other areas of optimal transport theory. In particular, our formulation makes it possible to introduce an appropriate notion of entropy regularization into the optimization problem, which in turn enables us to directly calculate optimal transport distances via a Sinkhorn-like method we call Sinkhorn Value Iteration (SVI). We show both theoretically and empirically that this method converges quickly to an optimal coupling, essentially at the same computational cost of running vanilla Sinkhorn in each pair of states. Along the way, we point out that our optimal transport distance exactly matches the common notion of bisimulation metrics between Markov chains, and thus our results also apply to computing such metrics, and in fact our algorithm turns out to be significantly more efficient than the best known methods developed so far for this purpose.

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not trivially extend to Generalized Planning (GP); GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in their number of objects, the initial and goal configuration of these objects and hence, in the number (and possible values) of the state variables. State-space search, as it is implemented by heuristic planners, becomes then impractical for GP. In this paper we adapt the planning as heuristic search paradigm to the generalization requirements of GP, and present the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines an upgraded version of our GP algorithm, called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space for GP. Lastly, the paper defines a set of evaluation and heuristic functions for BFGP that asses the structural complexity of the candidate GP solutions, as well as their fitness to a given input set of classical planning instances. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g. integers.

This paper introduces a general approach for synthesizing procedural models of the state-transitions of a given discrete system. The approach is general in that it accepts different target languages for modeling the state-transitions of a discrete system; different model acquisition tasks with different target languages, such as the synthesis of STRIPS action models, or the update rule of a cellular automaton, fit as particular instances of our general approach. We follow an inductive approach to synthesis meaning that a set of examples of state-transitions, represented as (pre-state, action, post-state) tuples, are given as input. The goal is to synthesize a structured program that, when executed on a given pre-state, outputs its associated post-state. Our synthesis method implements a combinatorial search in the space of well-structured terminating programs that can be built using a Random-Access Machine (RAM), with a minimalist instruction set, and a finite amount of memory. The combinatorial search is guided with functions that asses the complexity of the candidate programs, as well as their fitness to the given input set of examples.

Although heuristic search is one of the most successful approaches to classical planning, this planning paradigm does not apply straightforwardly to Generalized Planning (GP). This paper adapts the planning as heuristic search paradigm to the particularities of GP, and presents the first native heuristic search approach to GP. First, the paper defines a program-based solution space for GP that is independent of the number of planning instances in a GP problem, and the size of these instances. Second, the paper defines the BFGP algorithm for GP, that implements a best-first search in our program-based solution space, and that is guided by different evaluation and heuristic functions.

Landmarks are one of the most effective search heuristics for classical planning, but largely ignored in generalized planning. Generalized planning (GP) is usually addressed as a combinatorial search in a given space of algorithmic solutions, where candidate solutions are evaluated w.r.t. the instances they solve. This type of solution evaluation ignores any sub-goal information that is not explicit in the representation of the planning instances, causing plateaus in the space of candidate generalized plans. Furthermore, node expansion in GP is a run-time bottleneck since it requires evaluating every child node over the entire batch of classical planning instances in a GP problem. In this paper we define a landmark counting heuristic for GP (that considers sub-goal information that is not explicitly represented in the planning instances), and a novel heuristic search algorithm for GP (that we call PGP) and that progressively processes subsets of the planning instances of a GP problem. Our two orthogonal contributions are analyzed in an ablation study, showing that both improve the state-of-the-art in GP as heuristic search, and that both benefit from each other when used in combination.

Recognition in planning seeks to find agent intentions, goals or activities given a set of observations and a knowledge library (e.g. goal states, plans or domain theories). In this work we introduce the problem of Online Action Recognition. It consists in recognizing, in an open world, the planning action that best explains a partially observable state transition from a knowledge library of first-order STRIPS actions, which is initially empty. We frame this as an optimization problem, and propose two algorithms to address it: Action Unification (AU) and Online Action Recognition through Unification (OARU). The former builds on logic unification and generalizes two input actions using weighted partial MaxSAT. The latter looks for an action within the library that explains an observed transition. If there is such action, it generalizes it making use of AU, building in this way an AU hierarchy. Otherwise, OARU inserts a Trivial Grounded Action (TGA) in the library that explains just that transition. We report results on benchmarks from the International Planning Competition and PDDLGym, where OARU recognizes actions accurately with respect to expert knowledge, and shows real-time performance.

In this paper, we present a learning approach to facilitate the teaching of new board exercises to assistive robotic systems. We formulate the problem as the learning of action models using Boolean predicates, disjunctive preconditions, and existential quantifiers from demonstrations of successful exercise executions. To be able to cope with exercises whose rules depend on a set of features that are initialized at the beginning of each play-out, we introduce the concept of dynamic context. Furthermore, we show how the learnt knowledge can be represented intuitively in a graphical interface that helps the caregiver understand what the system has learnt. As validation, we conducted a user study in which we evaluated whether and to which extent different types of feedback can affect the subjects’ performance while teaching three types of exercises: (1) sorting numbers; (2) arranging letters; and (3) reproducing shapes sequences in reversed order. The results suggest that textual and graphical feedback are beneficial.

Generalized planning aims at computing an algorithm-like structure (generalized plan) that solves a set of multiple planning instances. In this paper we define negative examples for generalized planning as planning instances that must not be solved by a generalized plan. With this regard the paper extends the notion of validation of a generalized plan as the problem of verifying that a given generalized plan solves the set of input positives instances while it fails to solve a given input set of negative examples. This notion of plan validation allows us to define quantitative metrics to asses the generalization capacity of generalized plans. The paper also shows how to incorporate this new notion of plan validation into a compilation for plan synthesis that takes both positive and negative instances as input. Experiments show that incorporating negative examples can accelerate plan synthesis in several domains and leverage quantitative metrics to evaluate the generalization capacity of the synthesized plans.

Learning is usually performed by observing real robot executions. Physics-based simulators are a good alternative for providing highly valuable information while avoiding costly and potentially destructive robot executions. We present a novel approach for learning the probabilities of symbolic robot action outcomes. This is done leveraging different environments, such as physics-based simulators, in execution time. To this end, we propose MENID (Multiple Environment Noise Indeterministic Deictic) rules, a novel representation able to cope with the inherent uncertainties present in robotic tasks. MENID rules explicitly represent each possible outcomes of an action, keep memory of the source of the experience, and maintain the probability of success of each outcome. We also introduce an algorithm to distribute actions among environments, based on previous experiences and expected gain. Before using physics-based simulations, we propose a methodology for evaluating different simulation settings and determining the least time-consuming model that could be used while still producing coherent results. We demonstrate the validity of the approach in a dismantling use case, using a simulation with reduced quality as simulated system, and a simulation with full resolution where we add noise to the trajectories and some physical parameters as a representation of the real system.

Finite State Controllers (FSCs) are an effective way to compactly represent sequential plans. By imposing appropriate conditions on transitions, FSCs can also represent generalized plans (plans that solve a range of planning problems from a given domain). In this paper we introduce the concept of hierarchical FSCs for planning by allowing controllers to call other controllers. This call mechanism allows hierarchical FSCs to represent generalized plans more compactly than individual FSCs, to compute controllers in a modular fashion or even more, to compute recursive controllers. The paper introduces a classical planning compilation for computing hierarchical FSCs that solve challenging generalized planning tasks. The compilation takes as input a finite set of classical planning problems from a given domain. The output of the compilation is a single classical planning problem whose solution induces: (1) a hierarchical FSC and (2), the corresponding validation of that controller on the input classical planning problems.

This paper presents a novel approach for generating Context-Free Grammars (CFGs) from small sets of input strings (a single input string in some cases). Our approach is to compile this task into a classical planning problem whose solutions are sequences of actions that build and validate a CFG compliant with the input strings. In addition, we show that our compilation is suitable for implementing the two canonical tasks for CFGs, string production and string recognition.